Fernandes, who blasted a last-minute spot-kick against Aston Villa at Old Trafford on Saturday over the crossbar, which would have secured a point for United, posted a lengthy apology on social media.
"Nobody is more frustrated and disappointed than me for missing the penalty and the consequent defeat," he tweeted.
"I've always assumed my responsibilities and I've always embraced them under pressure in moments like this. Today, I failed. But I took a step forward and faced the challenge with the same ambition and responsibility as when, on the many other occasions, the ball ended up in the net.
"Criticism and contrasting opinions are a big part of football. I've learned to live with it, even using them to drive me on, and I consider it all a very important part of my commitment to never stop trying to improve and to become the best player I can possibly be, for me and the team.
"Today I once again took the responsibility given to me almost since I joined United and I will take it again without any fear or dread whenever called upon. The most important thing for me is to win together and I'll always do everything I can to help my teammates and the club to be the best we can be.
"I'm a player who leaves everything on the pitch, with great desire and commitment. And that's what I'll continue to do.
"Thank you for all your support after the final whistle! Hearing you chanting my name in the stadium was very emotional… I will come back stronger for me, because these are the standards I hold myself to, but most of all for my teammates and our fans who have always supported us."
But, in a Q&A on Twitter, Gary Neville has blasted apology tweets and the PR people surrounding them, claiming that players need to 'speak with authenticity' after defeats.
The former Manchester United full-back tweeted: "It's embarrassing! They need to sack their PR people, speak with some authenticity and get on with it.
"I'm going to go big on this in the next few weeks. They've all got these comms managers that are creating personalities that don't exist!"
He later tweeted, adding to his point: "The apology culture that's engulfing football would be ok if it came from a genuine place.
"However more often than not it's a smokescreen and diversion tactic designed to mask a crap performance by experts!
"Lose a game = crisis comms meet! How do we spin this one our way?"
He finalised by saying: "Final message of the day on the apology stuff and strong advice to players.
"If you're going to say something after a game, either go on TV (I accept players don't always want to) or post a video on social media where everyone can see it's you."